Calculate each value mentally. (24^2)(0.5^2)

Question

Accepted Answer

Welcome back. I am so glad you're here. We are Given this expression 32 squared times 0.125 squared. And we're asked to compute this cognitively. So we can't use a calculator. Well, how do we do that? Well, the first thing I notice here is this 0.125 that could be rewritten as 1/8. So we'd have 1/8 squared and that's still times squared. And now I call to mind the quotient to power rule. We recall from previous lessons that the quotient to power rule tells us that when we have a fraction raised to an exponent, then we could rewrite that as both the numerator and the denominator raised to that exponent. So that could be rewritten as one squared over eight squared and still times 32 squared. And now we can simplify our numerator because we know that one squared equals one. So we would have 32 squared times 1/8 squared. And we could put that 32 squared over one multiply these two fractions, multiplying the numerator straight across and we'd have 32 squared and multiply our denominators straight across and we'd have eight squared. And so now we have 32 squared over eight squared in that there's that quotient to power rule again. But this time in reverse. Now we have the same exponents in our numerator and our denominator. And we can pull those both outside of the parentheses. So we have the fraction in parentheses. 32 over eight. And that's all raised to the second power. Now we can do the division inside of the parentheses, 32 divided by eight, that equals four. So we have four squared, well four squared is 16. We look at our answer choices and this matches with answer choice C. Well done, we'll catch you on the next one.

Calculate each value mentally. (24^2)(0.5^2)

Key Concepts

Exponents

Multiplication of Powers

Fractional Exponents

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